พลังงานปฏิกิริยา, กิจกรรม และสมดุลการสลายตัว
GRE Subject Test · GRE Physics หัวข้อ 46 5:54 การบรรยายภาษาอังกฤษ · คำบรรยายภาษาอังกฤษ + 中文 ลอยตัวบนภาพ
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Transcript
One atomic mass unit is 931.5 mega electron volts, so a reaction energy is a small difference between large masses.
一个原子质量单位相当于 931.5 兆电子伏，所以反应能是两个大质量之间的微小差值。
This topic computes reaction energies from careful mass bookkeeping, turns a half-life into an activity, balances a decay chain, and compares fission with fusion.
本主题通过仔细的质量核算计算反应能，把半衰期换算成活度，平衡衰变链，并比较裂变与聚变。
The reaction energy is Q equals m initial minus m final, times c squared.
反应能 Q 等于初始质量减去最终质量，再乘以 c 的平方。
Q greater than zero releases kinetic energy.
Q 大于零时释放动能。
Track every species, and keep the mass convention consistent: tabulated atomic masses include electrons.
追踪所有粒子，并保持质量约定一致：表格中的原子质量包含电子。
For beta minus decay and for alpha decay with a neutral helium product, atomic electron counts balance directly. Beta plus or electron capture needs explicit electron-mass terms.
对于 β⁻ 衰变以及中性氦产物的 α 衰变，原子电子数直接平衡；β⁺ 或电子俘获则需要显式的电子质量项。
Use one u equals nine hundred thirty-one point five MeV per c squared.
使用 1 u = 931.5 MeV/c²。
Alpha decay of U-238 with atomic masses two hundred thirty-eight point zero five zero eight u, to two hundred thirty-four point zero four three six u plus four point zero zero two six u, gives delta m equals zero point zero zero four six u and Q approximately equals four point two eight MeV.
铀-238的α衰变，原子质量从238.0508 u变为234.0436 u加4.0026 u，质量差Δm为0.0046 u，释放能量Q约为4.28 MeV。
Fusion D plus T with two point zero one four one plus three point zero one six one minus four point zero zero two six minus one point zero zero eight seven equals zero point zero one eight nine u gives Q approximately equals seventeen point six MeV.
氘氚聚变D+T，质量计算为2.0141加3.0161减4.0026减1.0087等于0.0189 u，释放能量Q约为17.6 MeV。
A reaction also requires charge and nucleon-number balance. N-14 plus alpha to O-17 plus p balances seven plus two equals nine and fourteen plus four equals eighteen.
核反应还需满足电荷数与核子数守恒：氮-14加α粒子生成氧-17加质子，电荷数7加2等于9，核子数14加4等于18。
Activity is A equals lambda N, with decay constant lambda equal to the natural log of 2 over the half-life; one becquerel is one decay per second.
活度 A 等于 λ N，衰变常数 λ 等于 2 的自然对数除以半衰期；1 贝可勒尔等于每秒 1 次衰变。
For a half-life of 2 hours and N equal to 6 times 10 to the 12, A equals 6 times 10 to the 12, times the natural log of 2, over 7200, about 5.8 times 10 to the 8 becquerels.
半衰期为 2 小时、N 等于 6 乘以 10 的 12 次方时，A 等于 6 乘以 10 的 12 次方乘以 ln 2 再除以 7200，约为 5.8 乘以 10 的 8 次方贝可勒尔。
After three half-lives both N and A fall to one eighth.
经过三个半衰期后，N 和 A 都降为原来的八分之一。
Equal activities do not imply equal atom counts; a shorter half-life at fixed N gives a larger A.
活度相等并不意味着原子数相等：N 固定时，半衰期越短，活度越大。
In a chain A to B to C with a long-lived parent, where lambda sub A is much less than lambda sub B, B accumulates until its activity approaches the parent activity.
在A到B再到C的链式反应中，若母核寿命很长，即lambda_A远小于lambda_B，则B会不断积累，直到其活度趋近于母核活度。
This is called secular equilibrium.
这称为长期平衡。
Write the balance d N sub B by d t equals lambda sub A times N sub A minus lambda sub B times N sub B.
写出平衡方程：dN_B/dt等于lambda_A乘以N_A减去lambda_B乘以N_B。
The binding energy per nucleon curve peaks near iron.
比结合能曲线在铁附近达到峰值。
So heavy fission, about 7.6 to 8.5 MeV per nucleon over roughly 240 nucleons, of order 200 MeV, and light fusion both release energy.
因此，重核裂变（约每核子7.6至8.5 MeV，涉及约240个核子，总量级为200 MeV）和轻核聚变都会释放能量。
Compare total binding, not nucleon counts.
比较总结合能，而非核子数量。
Convert the 2 hour half-life to 7200 seconds first.
先把 2 小时的半衰期换算成 7200 秒。
Then the activity is ln 2 times 6 times 10 to the 12, over 7200: 5.78 times 10 to the 8 becquerel.
然后活度等于 ln 2 乘 6 乘 10 的 12 次方，再除以 7200：5.78 乘 10 的 8 次方贝可。
A daughter in a decay chain is made by the parent and lost by its own decay: its rate of change is lambda A N A minus lambda B N B.
衰变链中的子核由母核产生，又因自身衰变而减少：其变化率等于 λA NA 减 λB NB。
Equal activities do not mean equal populations.
活度相等并不意味着粒子数相等。
A parent has initial population N sub zero and daughter population zero.
母体初始数量为N零，子体初始数量为零。
Both decay constants equal lambda.
两者的衰变常数均等于lambda。
Derive daughter population and the time of its maximum.
推导子体数量及其达到最大值的时间。
Parent population is N sub A equals N sub 0 e to the minus lambda t.
母体数量为N_A等于N_0乘以e的负lambda t次方。
Daughter equation dot N sub B plus lambda N sub B equals lambda N sub 0 e to the minus lambda t has integrating factor e to the lambda t, giving N sub B equals lambda N sub 0 t e to the minus lambda t.
子体方程dot N_B加lambda N_B等于lambda N_0乘以e的负lambda t次方，其积分因子为e的lambda t次方，解得N_B等于lambda N_0 t乘以e的负lambda t次方。
Derivative is lambda N sub 0 e to the minus lambda t times 1 minus lambda t.
导数为lambda N_0乘以e的负lambda t次方乘以1减lambda t。
Maximum occurs at t equals 1 over lambda, with N sub B equals N sub 0 divided by e.
最大值出现在t等于1除以lambda时，此时N_B等于N_0除以e。
Award parent, equation, integrating factor, solution, maximum time and value.
评分点包括母体、方程、积分因子、解、最大时间及其对应值。
Direct use of an unequal decay constant formula would give a removable zero over zero limit.
直接使用不等衰变常数公式将得到一个可去零比零极限。
Mixing atomic and nuclear masses without tracking electrons, or reporting a positive Q for a reaction that needs energy input.
混合原子质量和核质量而未追踪电子，或为需要能量输入的反应报告正的Q值。
Balance charge and nucleon number first, then check the sign of Q.
首先配平电荷和核子数，然后检查Q的符号。
Q value: The rest-mass energy converted to kinetic energy in a reaction, m initial minus m final, times c squared.
Q值：反应中静止质量能转化为动能的部分，即m初始减m最终，乘以c平方。
Activity: The decay rate lambda N of a radioactive sample, measured in becquerel.
活度：放射性样品的衰变率λN，单位为贝克勒尔。
Retrieve the meanings without reading the definitions, then change a parameter in the original transfer and test the limiting case.
不阅读定义，凭记忆回忆其含义，然后更改原始传递中的一个参数，并检验极限情况。